Adaptive Multi-objective Optimizing Flight Controller

The problem of synthesizing online optimal flight controllers in the presence of multiple objectives is considered. A hybrid adaptive-optimal control architecture is presented, which is suitable for implementation on systems with fast, nonlinear and uncertain dynamics subject to constraints. The problem is cast as an adaptive Multi-Objective Optimization (MO-Op) flight control problem wherein control policy is sought that attempts to optimize over multiple, sometimes conflicting objectives. A solution strategy utilizing Gaussian Process (GP)-based adaptive-optimal control is presented, in which the system uncertainties are learned with an online updated budgeted GP. The mean of the GP is used to feedback-linearize the system and reference model shaping Model Predictive Control (MPC) is utilized for optimization. To make the MO-Op problem online-realizable, a relaxation strategy that poses some objectives as adaptively updated soft constraints is proposed. The strategy is validated on a nonlinear roll dynamics model with simulated state-dependent flexible-rigid mode interaction. In order to demonstrate low probability of failure in the presence of stochastic uncertainty and state constraints, we can take advantage of chance-constrained programming in Model Predictive Control. The results for the single objective case of chance-constrained MPC is also shown to reflect the low probability of constraint violation in safety critical systems such as aircrafts. Optimizing the system over multiple objectives is only one application of the adapive-optimal controller. Another application we considered using the adaptive-optimal controller setup is to design an architecture capable of adapting to the dynamics of different aerospace platforms. This architecture brings together three key elements, MPC-based reference command shaping, Gaussian Process (GP)-based Bayesian nonparametric Model Reference Adaptive Control (MRAC) which both were used in the previous application as well, and online GP clustering over nonstationary (time-varying) GPs. The key salient feature of our architecture is that not only can it detect changes, but it uses online GP clustering to enable the controller to utilize past learning of similar models to significantly reduce learning transients. Stability of the architecture is argued theoretically and performance is validated empirically.Mechanical & Aerospace Engineerin

Exact Pareto Optimal Search for Multi-Task Learning and Multi-Criteria Decision-Making

Given multiple non-convex objective functions and objective-specific weights, Chebyshev scalarization (CS) is a well-known approach to obtain an Exact Pareto Optimal (EPO), i.e., a solution on the Pareto front (PF) that intersects the ray defined by the inverse of the weights. First-order optimizers that use the CS formulation to find EPO solutions encounter practical problems of oscillations and stagnation that affect convergence. Moreover, when initialized with a PO solution, they do not guarantee a controlled trajectory that lies completely on the PF. These shortcomings lead to modeling limitations and computational inefficiency in multi-task learning (MTL) and multi-criteria decision-making (MCDM) methods that utilize CS for their underlying non-convex multi-objective optimization (MOO). To address these shortcomings, we design a new MOO method, EPO Search. We prove that EPO Search converges to an EPO solution and empirically illustrate its computational efficiency and robustness to initialization. When initialized on the PF, EPO Search can trace the PF and converge to the required EPO solution at a linear rate of convergence. Using EPO Search we develop new algorithms: PESA-EPO for approximating the PF in a posteriori MCDM, and GP-EPO for preference elicitation in interactive MCDM; experiments on benchmark datasets confirm their advantages over competing alternatives. EPO Search scales linearly with the number of decision variables which enables its use for training deep networks. Empirical results on real data from personalized medicine, e-commerce and hydrometeorology demonstrate the efficacy of EPO Search for deep MTL

On finding multiple pareto-optimal solutions using classical and evolutionary generating methods

In solving multi-objective optimization problems, evolutionary algorithms have been adequately applied to demonstrate that multiple and well-spread Pareto-optimal solutions can be found in a single simulation run. In this paper, we discuss and put together various different classical generating methods which are either quite well-known or are in oblivion due to publication in less accessible journals and some of which were even suggested before the inception of evolutionary methodologies. These generating methods specialize either in finding multiple Pareto-optimal solutions in a single simulation run or specialize in maintaining a good diversity by systematically solving a number of scalarizing problems. Most classical generating methodologies are classified into four groups mainly based on their working principles and one representative method from each group is chosen in the present study for a detailed discussion and for its performance comparison with a state-of-the-art evolutionary method. On visual comparisons of the efficient frontiers obtained for a number of two and three-objective test problems, the results bring out interesting insights about the strengths and weaknesses of these approaches. The results should motivate researchers to design hybrid multi-objective optimization algorithms which may be better than each of the individual methods

Tool and Process Design for Semi-dry Drilling of Steel: An Innovation for Green Manufacturing

The current trend in the metal-cutting industry is to find ways to completely eliminate or drastically reduce cutting fluid use in most machining operations. Recent advances in tool and machine technology have made it possible to perform some machining without cutting fluid use or with minimum quantity lubrication (MQL). Drilling takes a key position in the realization of dry or MQL machining. Economical mass machining of common metals (e.g., tool and construction-grade steels) requires knowledge of the work piece characteristics as well as the optimal machining conditions. In this study we investigated the effects of using MQL in drilling 1020 and 4140 steels using HSS tools with different coatings and geometries. The treatments selected for MQL in this study are commonly used by industry under flood cooling for these materials. A full factorial experiment was conducted, and the regression models for both surface finish and hole size were generated. The regression models were then used in a Pareto optimization study, and the trade-off between surface finish and hole size deviation from the nominal size was reported. The results showed a definite increase in tool life and better or very acceptable surface quality and size of holes drilled when usingMQL compared with flood cooling.ISTC Sponsored Research Program ; HWR05-192Ope

Hybrid Statistical and Engineering Optimization Architectures in Early Multidisciplinary Designs of Resilience and Expensive Black-box Complex Systems

Practical engineering design problems are generally multi-disciplinary with limited budget and high risk in terms of life loss, economic resources, etc. In the early phase of such problems, selection of true efficient designs is desired while minimizing overall design cost by avoiding expensive search processes. However, the task is difficult for a simple optimization framework due to the formulation complexity, high function evaluation cost, uncertain design parameters etc. Thus, the overall research goal is to develop complex, hybrid optimization architectures for solving early design problems considering the trade-off among model complexity, performance and cost. We start by comparing multiple architectures, and investigated a nested bi-level architecture for early resilience design with discrete design space and with a trade-off among multiple objectives at different risk level scenarios. The work then focused on increased problem complexity with black-box functions in a mechanical design classification problem with discontinuous design space using a sequential Bayesian Optimization (BO) architecture to locate an unknown creep-fatigue failure constraint boundary. The work then extends a weighted Tchebycheff black-box multi-objective BO (MO-BO) architecture for mechanical design with a trade-off between design risk and cost, with model calibration through regression analysis of unknown parameters. Finally, we investigate an iterative regression model selection procedure, nested into the proposed MO-BO, to enhance design flexibility, estimation and overall performance. This work can be applicable to any domains of complex or/and expensive black-box system design problems

Numerical and Evolutionary Optimization 2020

This book was established after the 8th International Workshop on Numerical and Evolutionary Optimization (NEO), representing a collection of papers on the intersection of the two research areas covered at this workshop: numerical optimization and evolutionary search techniques. While focusing on the design of fast and reliable methods lying across these two paradigms, the resulting techniques are strongly applicable to a broad class of real-world problems, such as pattern recognition, routing, energy, lines of production, prediction, and modeling, among others. This volume is intended to serve as a useful reference for mathematicians, engineers, and computer scientists to explore current issues and solutions emerging from these mathematical and computational methods and their applications

Método NBI-EQMM com restrições multivariadas para otimização do processo de Torneamento Duro.

Esta tese apresenta o desenvolvimento e a avaliação do método NBI-EQMM com restrições multivariadas para problemas de otimização multiobjetivo não-linear de larga escala, com funções objetivo e restrições correlacionadas. No método, a seleção das funções que integram cada grupo é realizada aplicando-se a Análise Hierárquica de Cluster (AHC) assistida por uma matriz de distâncias. Para testar a adequação da proposta, um arranjo composto central (CCD) com 3 variáveis de entrada (x) e 22 respostas (Y) foi desenvolvido com vistas a otimizar o processo de torneamento do aço endurecido ABNT H13, usinado com as ferramentas Wiper PCBN 7025AWG, CC 6050WG e CC 650WG. As 22 superfícies de resposta foram definidas para que o problema pudesse contemplar cinco dimensões de um processo real, em escala industrial: qualidade, custo, produtividade, viabilidade econômica e financeira e sustentabilidade. Os resultados obtidos indicam que o método NBI-EQMM com restrições multivariadas de igualdade e desigualdade contribuiu para a formação de fronteiras equiespaçadas e sem inversão dos sinais de correlação das respostas originais, conduzindo todas as respostas para valores próximos aos seus alvos, sem desrespeitar as restrições multivariadas pré-estabelecidas. Foi observado que a inclusão das restrições multivariadas para o cálculo da matriz Payoff permite o reescalonamento da fronteira de Pareto, aproximando as soluções ótimas obtidas de seus ótimos individuais, evitando que soluções Pareto-ótimo fora da região de solução viável sejam obtidas. Observou-se ainda que, quando os eixos da fronteira de Pareto são formados por respostas positivamente correlacionadas e com o mesmo sentido de otimização ou negativamente correlacionadas e com o sentido de otimização diferente, o método NBI bivariado falha, corroborando, portanto, a necessidade de aplicação do método NBI-EQMM proposto. Considerando que um importante fator para a competitividade das organizações é a fabricação de produtos em grande escala, com custo mínimo e aliada a padrões de qualidade compatíveis aos exigidos pelos clientes, pode-se dizer que a ferramenta CC 6050WG conseguiu atender, simultaneamente, a todas essas características, sendo, portanto, considerada a mais eficiente entre as ferramentas analisadas nesta Tese

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Optimisation multiobjectif -- Algorithme de résolution pour la programmation biobjectif -- Sélection optimale d'un portefeuille en finance -- Algorithme de résolution pour la programmation multiobjectif